Despite repeated statements by Republican political leaders that American elections are rife with illegal voting, credible reports of fraud have been hard to find and convictions rarer still.

That may help explain the unusually heavy penalty imposed on Rosa Maria Ortega, 37, a permanent resident and a mother of four who lives outside Dallas. On Thursday, a Fort Worth judge sentenced her to eight years in prison — and almost certainly, deportation later — after she voted illegally in elections in 2012 and 2014.